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Amy receives a home improvement loan of $10,000. The loan has a nominal interest rate convertible...

  1. Amy receives a home improvement loan of $10,000. The loan has a nominal interest rate convertible monthly of i(12) = 6%. The term of the loan is three years and Amy is expected to make level end-of-month payments, except that she is allowed to miss one payment so long as she then pays higher level payments for the remainder of the three years, so as to have repaid the loan at the end of the three-year period. Suppose Amy misses the payment at the end of the eleventh month.

    a) At the end of eleven months, without any payment having been made at that time, what is the outstanding loan balance?

    b) What must the new level payments be?

Solutions

Expert Solution

Original loan amount = $10,000

Annual interest rate = 6%

Monthly interest rate = 6%/12 = 0.5%

Loan period = 3 years = 36 months

Level monthly payments can be calculated using the formula for an ordinary annuity

PV = loan amount = $10,000

i = Monthly interest rate = 0.5%

n = Loan period = 36 months

C = $304.22

Original monthly payment = $304.22

a)

Outstanding loan balance after 10 months can be calculated using the PV for ordinary annuity formula

C = Original monthly payment = $304.22

i = Monthly interest rate = 0.5%

n = Remaining Loan period = 36 - 10 months = 26 months

PV = $7,399.84

Outstanding loan balance after 10 months = $7,399.84

Outstanding loan balance after 11 months = Outstanding loan balance after 10 months + Interest for the 11th month

= $7,399.84 + 0.5% of $7,399.84 = $7,399.84 *(1+0.5%) = $7,436.84

Outstanding loan balance after 11 months = $7,436.84

b)

New Level monthly payments can be calculated using the formula for an ordinary annuity

PV = Outstanding loan balance after 11 months = $7,436.84

i = Monthly interest rate = 0.5%

n = Remaining Loan period = 36 - 11 months = 25 months

C = $317.19

New level monthly payment = $317.19

jeff jeffy answered 2 years ago
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